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:
- Start with the slope-intercept formula: [tex]y = mx + b.[/tex]
- Plug in the slope and the coordinates of the given point: [tex]3 = (¾)(-8) + b.[/tex]
- 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]
- 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.