Question

What is the y-intercept of the line perpendicular to the line y = four thirdsx + 1 that includes the point (4, 1)?

2

negative 13 over 3

4

negative 19 over 3

Answer 1

Answer:

4

Step-by-step explanation:

We'll begin by calculating the slope of the equation. This is illustrated below:

y = 4/3x + 1

Comparing the above equation with:

y = mx + c

The slope (m) of line is 4/3.

Next, we shall determine the slope of the equation perpendicular to:

y = 4/3x + 1

This is illustrated below:

When two lines are perpendicular, their slope are related as:

m2 = – 1/m1

From the above, m1 = 4/3

m2 = –1 ÷ 4/3

m2 = –1 × 3/4

m2 = – 3/4

Next, we shall determine the equation passing through (4, 1). This is illustrated below:

y – y1 = m(x – x1)

y1 = 1

x1 = 4

m = – 3/4

y – y1 = m(x – x1)

y – 1 = –3/4 (x – 4)

y – 1 = –3/4x + 3

y = –3/4x + 3 + 1

y = –3/4x + 4

Comparing:

y = –3/4x + 4 with y = mx + c

The y-intercept, c is 4.

Answer 2

The y-intercept of a function is the point where the function has an x value of 0

The y-intercept is (c) 4

The equation is given as:

$y = \frac 43x + 1$

The slope (m) of the above equation is:

$m = \frac 43$

The slope of the line perpendicular to the given equation is:

$m = -\frac 34$

From the question, the line passes through (4,1).

So, the equation is calculated as:

$y = m(x - x_1) + y_1$

This gives

$y = -\frac 34(x - 4) + 1$

Substitute 0 for x, to calculate the y-intercept

$y = -\frac 34(0 - 4) + 1$

$y = -\frac 34( - 4) + 1$

$y =3+1$

$y=4$

Hence, the y-intercept is (c) 4

Read more about y-intercepts at:

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