PSAT Math - Slope and Line Equations

$\textup{What is the slope of a line perpendicular to the line with the equation}$

$3y+2x=6\textup{ ?}$

$\frac{3}{2}$

$\frac{-3}{2}$

$\frac{-2}{3}$

$\frac{2}{3}$

$\textup{Connot be determined with this information.}$

Explanation

$\textup{Get into }y=mx+b\textup{ format: }3y=-2x+6:,:y=-\frac{2}{3}x+2$

$\textup{Perpendicular slope is negative reciprocal of }-\frac{2}{3}: \rightarrow \rightarrow \frac{3}{2}$

$\textup{What is the slope of a line perpendicular to the line with the equation}$

$3y+2x=6\textup{ ?}$

$\frac{3}{2}$

$\frac{-3}{2}$

$\frac{-2}{3}$

$\frac{2}{3}$

$\textup{Connot be determined with this information.}$

Explanation

$\textup{Get into }y=mx+b\textup{ format: }3y=-2x+6:,:y=-\frac{2}{3}x+2$

$\textup{Perpendicular slope is negative reciprocal of }-\frac{2}{3}: \rightarrow \rightarrow \frac{3}{2}$

Whast line goes through the points and ?

Explanation

Let $P_{1}=(1,3)$ and $P_{2}=(7,5)$

The slope is geven by: $m = (y_{2} - y_{1}) \div (x_{2} - x_{1})$ so

$m=\frac{1}{3}$

Then we use the slope-intercept form of an equation; so

$b=\frac{8}{3}$

And we convert

$y=\frac{1}{3}x+\frac{8}{3}$

to standard form.

Whast line goes through the points and ?

Explanation

Let $P_{1}=(1,3)$ and $P_{2}=(7,5)$

The slope is geven by: $m = (y_{2} - y_{1}) \div (x_{2} - x_{1})$ so

$m=\frac{1}{3}$

Then we use the slope-intercept form of an equation; so

$b=\frac{8}{3}$

And we convert

$y=\frac{1}{3}x+\frac{8}{3}$

to standard form.

What is the slope of a line that runs through points: (-2, 5) and (1, 7)?

2/3

5/7

3/2

Explanation

The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).

To calculate the slope of a line, use the following formula: Actmath_7_113_q7

What is the slope of a line that runs through points: (-2, 5) and (1, 7)?

2/3

5/7

3/2

Explanation

The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).

To calculate the slope of a line, use the following formula: Actmath_7_113_q7

Axes

Refer to above red line. What is its slope?

$\frac{1}{3}$

$-\frac{1}{3}$

Explanation

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{3} = 3$

Axes

Refer to above red line. What is its slope?

$\frac{1}{3}$

$-\frac{1}{3}$

Explanation

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{3} = 3$

What is the equation of the line with a negative slope that passes through the y-intercept and one x-intercept of the graph y = –x_2 – 2_x + 8 ?

y = –4_x_ + 8

y = –x + 8

y = –2_x_ + 8

y = –2_x_ + 4

y = –4_x_ + 4

Explanation

In order to find the equation of the line, we need to find two points on the line. We are told that the line passes through the y-intercept and one x-intercept of y = –x_2 – 2_x + 8.

First, let's find the y-intercept, which occurs where x = 0. We can substitute x = 0 into our equation for y.

y = –(0)2 – 2(0) + 8 = 8

The y-intercept occurs at (0,8).

To determine the x-intercepts, we can set y = 0 and solve for x.

0 = –x_2 – 2_x + 8

–x_2 – 2_x + 8 = 0

Multiply both sides by –1 to minimize the number of negative coefficients.

x_2 + 2_x – 8 = 0

We can factor this by thinking of two numbers that multiply to give us –8 and add to give us 2. Those numbers are 4 and –2.

x_2 + 2_x – 8= (x + 4)(x – 2) = 0

Set each factor equal to zero.

x + 4 = 0

Subtract 4.

x = –4

Now set x – 2 = 0. Add 2 to both sides.

x = 2

The x-intercepts are (–4,0) and (2,0).

However, we don't know which x-intercept the line passes through. But, we are told that the line has a negative slope. This means it must pass through (2,0).

The line passes through (0,8) and (2,0).

We can use slope-intercept form to write the equation of the line. According to slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept. We already know that b = 8, since the y-intercept is at (0,8). Now, all we need is the slope, which we can find by using the following formula:

m = (0 – 8)/(2 – 0) = –8/2 = –4

y = mx + b = –4_x_ + 8

The answer is y = –4_x_ + 8.

A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?

–2/3

–2/5

2/5

2/3

-3/5

Explanation

The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5

Slope and Line Equations

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