Answer :

Answer:

y = 3/4 x +9

Step-by-step explanation:

The slope is 3/4 and a point on the line is (-8,3).

The 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

Substituting the point into the equation and solving for b

3 = 3/4 (-8) + b

3 = -6+b

9 = b

The equation becomes:

y = 3/4 x +9

Final answer:

The equation of the line in slope-intercept form that passes through the point (-8, 3) with a slope of 3/4 is [tex]y = (3/4)x + 9.[/tex]

Explanation:

To write an equation in slope-intercept form for a line that passes through the point (-8, 3) with a slope of ¾, we use the slope-intercept equation of a line, which is  [tex]y = mx + b[/tex], where 'm' is the slope and 'b' is the y-intercept. We already have the slope (m = ¾), and we can plug in the point (-8, 3) to find 'b'.

ere are the steps to find the equation:

  1. Start with the slope-intercept formula: [tex]y = mx + b.[/tex]
  2. Plug in the slope and the coordinates of the given point: [tex]3 = (¾)(-8) + b.[/tex]
  3. Solve for 'b' by multiplying ¾ by -8 and then adding the result to both sides to isolate

[tex]'b': 3 = -6 + b ⇒ b = 3 + 6 ⇒ b = 9.[/tex]

  1. Now that we have the value of 'b', we can write the final equation: [tex]y = (¾)x + 9.[/tex]

This is the equation of the line in slope-intercept form with the slope of ¾ and y-intercept at 9.