Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form (-3,5). (3.3)

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asked Jan 22, 2022 219k views

2 Answers

Gonzaloriestra · Answer 1 · 2022-01-27T10:48:16+0000

Answer:

Point-slope form:

$\displaystyle y-3=-(1)/(3)(x-3)$

Slope-intercept form:

$\displaystyle y=-(1)/(3)x+4$

Explanation:

We want the equation in point-slope form and slope-intercept form that passes through the points (-3, 5) and (3, 3).

First, we will find the slope between the two points. By the slope formula:

$\displaystyle m=(5-3)/(-3-3)=(2)/(-6)=-(1)/(3)$

Point-slope form is given by:

$\displaystyle y-y_1=m(x-x_1)$

We can choose either point. I'm going to let (3, 3) be (x₁, y₁). The slope m is -1/3. Therefore:

$\displaystyle y-3=-(1)/(3)(x-3)$

Is the point-slope form*.

To find the slope-intercept form, we simply need to isolate y. Distribute:

$\displaystyle y-3=-(1)/(3)x+1$

Adding 3 to both sides yields:

$\displaystyle y=-(1)/(3)x+4$

This is slope-intercept form.

*If you use the other point, the point-slope form will be:

$\displaystyle y-5=-(1)/(3)(x+3)$