The equation of the line is [tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex]
The y - intercept of the equation is [tex]\frac{15}{4}[/tex]
Explanation:
Given that the equation of the line is [tex]y=4 x+1[/tex] and the slope is [tex]m=-\frac{1}{4}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (-1,4) and the slope [tex]m=-\frac{1}{4}[/tex] , we get,
[tex]y-4=-\frac{1}{4}(x+1)[/tex]
Simplifying, we get,
[tex]y-4=-\frac{1}{4}x-\frac{1}{4}[/tex]
[tex]y=-\frac{1}{4}x-\frac{1}{4}+4[/tex]
[tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex]
y - intercept:
The y - intercept of the equation is value of y when x = 0
Hence, substituting x = 0 in the equation [tex]y=-\frac{1}{4}x+\frac{15}{4}[/tex], we get,
[tex]y=-\frac{1}{4}(0)+\frac{15}{4}[/tex]
[tex]y=\frac{15}{4}[/tex]
Thus, the y - intercept of the equation is [tex]\frac{15}{4}[/tex]
