Question

Write the slope-intercept form of the line passing through (–8, –5) and (4, 4).

Answer 1

Answer:

$\huge\boxed{y = \frac{3}{4}x+1}$

Step-by-step explanation:

Finding the slope (m) first:

Given the coordinates (-8 , -5) and ( 4 , 4 )

Slope = $\sf \frac{Rise}{Run}$

Slope = $\sf \frac{y2-y1}{x2-x1}$

Slope = $\frac{4 + 8}{4+5}$

Slope = $\frac{12}{9}$

Slope = m = $\frac{3}{4}$

Finding y - intercept (b) :

Taking a coordinate say (4,4)

And putting it in slope intercept form along with b

y = mx+b

Where y = 4 , m = 3/4 and x = 4

4 = (3/4)(4) + b

4 = 3+b

4-3 = b

1 = b

So,

b = 1

Putting m and b now in slope-intercept equation:

y = mx+b

$y = \frac{3}{4}x+1$

Answer 2

Answer:

$\Huge \boxed{y=\frac{3}{4} x+1}$

$\rule[225]{225}{2}$

Step-by-step explanation:

We can find the slope through two points.

m = (y2 - y1)/(x2 - x1)

m = (4 - -5)/(4 - -8)

m = 9/12 = 3/4

The slope of the line is 3/4.

Slope-intercept form of a line is y=mx+b. Where m is the slope and b is the y-intercept.

y = 3/4x + b

A point on the line is (4, 4). x = 4 and y =4.

4 = 3/4(4) + b

4 = 3 + b

b = 1

The y-intercept is 1.

$\rule[225]{225}{2}$