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:  The correct options are(A) y-intercept is -1.(B) the slope-intercept form is y = 4x - 1.(D) The point [tex]\left(\dfrac{3}{8},\dfrac{1}{2}\right)[/tex] corresponds to [tex](x_1,y_1)[/tex] 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 [tex]\left(\dfrac{3}{8},\dfrac{1}{2}\right).[/tex]We are to select the statements that are true about the given line.We know thatthe slope-intercept form of the equation of a line is given by[tex]y=mx+c,[/tex]where m is the slope and c is the y-intercept.And, the point-slope form of the equation of a line 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 the line.So, the point-slope form of the given line is[tex]y-\dfrac{1}{2}=4\left(x-\dfrac{3}{8}\right).[/tex]That is, option (C) is incorrect and option (D) is CORRECT.Now, the slope-intercept form of the equation of given line is[tex]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.[/tex]Comparing with the slope-intercept form, we gety-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 [tex]\left(\dfrac{3}{8},\dfrac{1}{2}\right)[/tex] corresponds to [tex](x_1,y_1)[/tex] in the point-slope form of the equation.