Question

write an equation in slope intercept form of the line with the given characteristics: a) passes through (-3,0) and (-5,-3)

Answer 1

The equation of the line in slope-intercept form is $\bf{y= \frac{3}{2} x + \frac{9}{4}}$.

What is slope-intercept form?

• y=mx +c, where m is the slope and c is the y-intercept

Steps

1. Find the slope
2. Substitute value of the slope into the equation
3. Substitute a pair of coordinates
4. Solve for c
5. Rewrite equation with value of m and c

Working

The first step is to calculate the slope of the line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope

$= \frac{ - 3 - 0}{ - 5 -( - 3)}$

$= \frac{ - 3}{ - 5 + 3}$

$= \frac{ - 3}{ - 2}$

$= \frac{3}{2}$

Substitute the value of m into y= mx +c:

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

Next, substitute a pair of coordinates that the line passes through. Here, I will substitute (-3, 0) into the equation.

When x= -3, y= 0,

$0 = \frac{3}{2} ( - 3) + c$

Find the value of c:

$0 = - \frac{9}{2} + c$

$c = \frac{9}{2}$

Substitute the value of c into the equation:

Thus, the equation of the line is $y = \frac{3}{2} x + \frac{9}{2}$.

To learn more about slope-intercept form, check out: brainly.com/question/24436844.