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

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Leora03

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

  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.

[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.

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