PSAT Math - How to find slope of a line

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

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

$\frac{3}{2}$

$\frac{-3}{2}$

$\frac{-2}{3}$

$\frac{2}{3}$

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

Explanation

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

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

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

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

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

Which of the following lines intersects the y-axis at a thirty degree angle?

y = x

y = x - √2

y = x√2 - 2

y = x√3 + 2

y = x((√3)/3) + 1

Explanation

Line_intersect1

Line_intersect2

What is a possible slope of line y?

–2

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small -\frac{1}{2}$

Explanation

The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change in y divided by the change in x. The change in y is greater than the change in x, which implies that the slope must be less than –1, leaving –2 as the only possible solution.

What is the slope between and ?

$-\frac{4}{3}$

$\frac{2}{5}$

$\frac{1}{6}$

$\frac{3}{4}$

$-\frac{5}{2}$

Explanation

Let $P_{1}=(8,3)$ and $P_{2}=(5,7)$

$m = (y_{2} - y_{1}) \div (x_{2} - x_{1})$ so the slope becomes $-\frac{4}{3}$ .

Based on the table below, when x = 5, y will equal

x	y
-1	3
0	1
1	-1
2	-3

–11

–10

–9

Explanation

Use 2 points from the chart to find the equation of the line.

Example: (–1, 3) and (1, –1)

Using the formula for the slope, we find the slope to be –2. Putting that into our equation for a line we get y = –2x + b. Plug in one of the points for x and y into this equation in order to find b. b = 1.

The equation then will be: y = –2x + 1.

Plug in 5 for x in order to find y.

y = –2(5) + 1

y = –9

Which of the following equations has as its graph a line with slope 4?