You are given a line that has a slope of 4 and passes through the point (StartFraction 3 Over 8 EndFraction, one-half). Which statements about the equation of the line are true? Check all that apply.
The y-intercept is -1.
The slope-intercept equation is y = 4 x minus 1.
The point-slope equation is y minus StartFraction 3 Over 8 EndFraction = 4 (x minus one-half).
The Point (StartFraction 3 Over 8 EndFraction, one-half) corresponds to (x1

(A) The y-intercept is -1.
(B) The slope-intercept form is y = 4x - 1.
(D) The point [tex](\frac{3}{8} ,\frac{1}{2} )[/tex] corresponds to [tex](x_{1} ,y_{1} )[/tex] the point-slope form of the equation.

Fraction:

A fraction is a number that in mathematics represents a portion of a whole.
There are two parts: a numerator and a denominator.
The denominator is the total number of pieces that make up the whole, while the numerator is the number of equally sized portions of the whole.

Slope:

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
The letter m is frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line as "[tex]y=mx+b[/tex]" and "[tex]y=mx+c[/tex]," respectively.

Explanation -

We are given a line that passes through the point [tex](\frac{3}{8} ,\frac{1}{2} )[/tex] and has a slope of 4.

We must choose the claims regarding the provided line that are accurate.

The fact that the equation of a line in its slope-intercept form is given by [tex]y=mx+c[/tex].

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

Additionally, the equation of a line in point-slope form is [tex]y-y_{1} =m(x-x_{1} )[/tex] where m is the slope and [tex](x_{1} ,y_{1} )[/tex] is a point on a line.

So, the point-slope form of the given line is [tex]y-\frac{1}{2} =4(x-\frac{3}{8})[/tex].

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

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

[tex]y-\frac{1}{2} =4(x-\frac{3}{8} )\\[/tex]

⇒ [tex]y-\frac{1}{2} =4x-\frac{3}{2}[/tex]

⇒ [tex]y=4x-\frac{3}{2} +\frac{1}{2}[/tex]

⇒ [tex]y=4x-1[/tex]

With respect to the slope-intercept form, we obtain

The provided line's equation's y-intercept is equal to -1.

Hence, choices (A) and (B) are RIGHT.

Therefore, true statements about the equation are as follows:

(A) The y-intercept is -1.
(B) The slope-intercept form is y = 4x - 1.
(D) The point [tex](\frac{3}{8} ,\frac{1}{2} )[/tex] corresponds to [tex](x_{1} ,y_{1} )[/tex] the point-slope form of the equation.

Know more about slope-intercept form here:

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