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natulia [17]
3 years ago
11

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

Mathematics
1 answer:
kompoz [17]3 years ago
4 0

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

<u>Point-slope form:</u>

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.

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