ACT Math - How to find the equation of a line

Let y = 3_x_ – 6.

At what point does the line above intersect the following:

$2x =\frac{2}{3}y+4$

They do not intersect

They intersect at all points

(0,–1)

(–5,6)

(–3,–3)

Explanation

If we rearrange the second equation it is the same as the first equation. They are the same line.

Which of the following is the equation of a line between the points and ?

Explanation

Since you have y-intercept, this is very easy. You merely need to find the slope. Then you can use the form to find one version of the line.

The slope is:

$\frac{rise}{run} = \frac{y_1-y_0}{x_1-x_0}$

Thus, for the points and , it is:

$\frac{15-3}{4-0}= \frac{12}{4}=3$

Thus, one form of our line is:

If you move the to the left side, you get:

, which is one of your options.

What line goes through the points (1, 3) and (3, 6)?

3x + 5y = 2

2x – 3y = 5

4x – 5y = 4

–3x + 2y = 3

–2x + 2y = 3

Explanation

If P1(1, 3) and P2(3, 6), then calculate the slope by m = rise/run = (y2 – y1)/(x2 – x1) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

$\dpi{100} \small y=4x-6$

$\dpi{100} \small y=4x+6$

$\dpi{100} \small y=2x-3$

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=-2x+3$

Explanation

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

Which of the following equations does NOT represent a line?

Explanation

The answer is .

A line can only be represented in the form or , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

represents a parabola, not a line. Lines will never contain an term.

Given the graph of the line below, find the equation of the line.

Act_math_160_04

$y=\frac{10}{3}x-4$

Explanation

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

What is an equation of the line going through points and ?