Question

You are given a line that has a slope of 4 and passes through the point (3/8, 1/2) Which statements about the equation of the line are true? Check all that apply.


(A) The y-intercept is -1


(B) The slope-intercept equation is y = 4x-1


(C) The point-slope equation is y - 3/8 = 4(x-1/2)


(D) The Point (3/8, 1/2) corresponds to (x1, y1) in the point-slope form of the equation.

Answer 1

Answer:  The correct options are

(A) y-intercept is -1.

(B) the slope-intercept form is y = 4x - 1.

(D) The point $\left(\dfrac{3}{8},\dfrac{1}{2}\right)$ corresponds to $(x_1,y_1)$ in the point-slope form of the equation.

Step-by-step explanation:  We are given a line that has the slope of 4 and passes through the point $\left(\dfrac{3}{8},\dfrac{1}{2}\right).$

We are to select the statements that are true about the given line.

We know that

the slope-intercept form of the equation of a line is given by

$y=mx+c,$

where m is the slope and c is the y-intercept.

And, the point-slope form of the equation of a line is

$y-y_1=m(x-x_1),$ where m is the slope and $(x_1,y_1)$ is a point on the line.

So, the point-slope form of the given line is

$y-\dfrac{1}{2}=4\left(x-\dfrac{3}{8}\right).$

That is, option (C) is incorrect and option (D) is CORRECT.

Now, the slope-intercept form of the equation of given line is

$y-\dfrac{1}{2}=4\left(x-\dfrac{3}{8}\right)\\\\\\\Rightarrow y-\dfrac{1}{2}=4x-\dfrac{3}{2}\\\\\\\Rightarrow y=4x-\dfrac{3}{2}+\dfrac{1}{2}\\\\\Rightarrow y=4x-1.$

Comparing with the slope-intercept form, we get

y-intercept of the equation of given line = -1.

So, options (A) and (B) are CORRECT.

Thus, the correct options are

(A) y-intercept is -1.

(B) the slope-intercept form is y = 4x - 1.

(D) The point $\left(\dfrac{3}{8},\dfrac{1}{2}\right)$ corresponds to $(x_1,y_1)$ in the point-slope form of the equation.

Answer 2

Answer:

A,B,D are the answers

Step-by-step explanation: