The equation of the line in slope-intercept form is [tex]\bf{y= \frac{3}{2} x + \frac{9}{4}} [/tex].
What is slope-intercept form?
- y=mx +c, where m is the slope and c is the y-intercept
Steps
- Find the slope
- Substitute value of the slope into the equation
- Substitute a pair of coordinates
- Solve for c
- Rewrite equation with value of m and c
Working
The first step is to calculate the slope of the line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope
[tex] = \frac{ - 3 - 0}{ - 5 -( - 3)} [/tex]
[tex] = \frac{ - 3}{ - 5 + 3} [/tex]
[tex] = \frac{ - 3}{ - 2} [/tex]
[tex] = \frac{3}{2} [/tex]
Substitute the value of m into y= mx +c:
[tex]y = \frac{3}{2} x + c[/tex]
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,
[tex]0 = \frac{3}{2} ( - 3) + c[/tex]
Find the value of c:
[tex]0 = - \frac{9}{2} + c[/tex]
[tex]c = \frac{9}{2} [/tex]
Substitute the value of c into the equation:
Thus, the equation of the line is [tex]y = \frac{3}{2} x + \frac{9}{2} [/tex].
To learn more about slope-intercept form, check out: https://brainly.com/question/24436844.
