Question

An equation of a line through (-1,4) which is perpendicular to the line y = 4x + 1 and the slope is -1/4 what is the y-intercept

Answer 1

The equation of the line is $y=-\frac{1}{4}x+\frac{15}{4}$

The y - intercept of the equation is $\frac{15}{4}$

Explanation:

Given that the equation of the line is $y=4 x+1$ and the slope is $m=-\frac{1}{4}$

Equation of the line:

The equation of the line can be determined using the formula,

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

Substituting the point (-1,4) and the slope $m=-\frac{1}{4}$ , we get,

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

Simplifying, we get,

$y-4=-\frac{1}{4}x-\frac{1}{4}$

     $y=-\frac{1}{4}x-\frac{1}{4}+4$

     $y=-\frac{1}{4}x+\frac{15}{4}$

Thus, the equation of the line is $y=-\frac{1}{4}x+\frac{15}{4}$

y - intercept:

The y - intercept of the equation is value of y when x = 0

Hence, substituting x = 0 in the equation $y=-\frac{1}{4}x+\frac{15}{4}$, we get,

$y=-\frac{1}{4}(0)+\frac{15}{4}$

$y=\frac{15}{4}$

Thus, the y - intercept of the equation is $\frac{15}{4}$