Discover the Algebraic Equation of a Line Parallel to y=-3/4x+2 Through (8,2)

Question

Given the line parallel to the line

y=34x+2 y=-\frac{3}{4}x+2

and passes through the point (8,2) (8,2) .

Which of the algebraic representations is the corresponding one for the given line?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function
00:03 This is the slope of the line
00:08 Parallel lines have identical slopes
00:17 Let's use the line equation
00:25 Substitute the point according to the given data
00:32 Substitute the line's slope according to the given data
00:41 Continue solving to find the intersection point
00:48 This is the intersection point with the Y-axis
00:55 Now substitute the intersection point and slope in the line equation
01:05 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll determine the equation of the line that is parallel to y=34x+2 y = -\frac{3}{4}x+2 and passes through the point (8,2) (8,2) .

Step 1: Identify the slope of the given line.
The slope (m m ) of the line y=34x+2 y = -\frac{3}{4}x + 2 is 34-\frac{3}{4}, as it's the coefficient of x x .

Step 2: Use the point-slope form, yy1=m(xx1) y - y_1 = m(x - x_1) , where m=34 m = -\frac{3}{4} and the point (x1,y1)=(8,2) (x_1, y_1) = (8, 2) .

Substitute into the point-slope form:
y2=34(x8) y - 2 = -\frac{3}{4}(x - 8)

Step 3: Simplify this equation to obtain the slope-intercept form:
y2=34x+34×8 y - 2 = -\frac{3}{4}x + \frac{3}{4} \times 8

Calculate the right side:
y2=34x+6 y - 2 = -\frac{3}{4}x + 6

Add 2 to both sides to isolate y y :
y=34x+6+2 y = -\frac{3}{4}x + 6 + 2
y=34x+8 y = -\frac{3}{4}x + 8

This equation, y=34x+8 y = -\frac{3}{4}x + 8 , is in slope-intercept form and matches choice 4.

Thus, the equation of the line parallel to y=34x+2 y = -\frac{3}{4}x + 2 and passing through (8,2) (8, 2) is y=34x+8\boxed{y = -\frac{3}{4}x + 8}.

Answer

y=34x+8 y=-\frac{3}{4}x+8