Question

Write the slip-intercept form of the equation of the line described

Answer 1

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

Point-slope form:

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= $\frac{5}{6}$

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

$1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3}$

Thus the equation of the line is $y = \frac{5}{6} x - 2 \frac{1}{3}$.

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

= -1 ÷ (-⅜)

= -1 ×(-8/3)

= $\frac{8}{3}$

$y = \frac{8}{3} x + c$

When x=3, y=3,

$3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5$

Thus the equation of the line is $y = \frac{8}{3} x - 5$.