Question

Write the slope-intercept form of the equation of the line through the given point with the

given slope.
through: (-2,3), slope = -5/7

Answer 1

y=−0.7x+1.6.

Step-by-step explanation:

Plug the slope and the x and y of the given point into y = mx + b, then solve for b.

Slope: −0.7

Point: ( −2 , 3 )

y=mx+b

3=−0.7( −2 )+b

3=1.4+b

b=1.6

Step 2. Replace m and b with their values in the y=mx+b formula.

y=mx+b

y=−0.7x+1.6

The slope-intercept form equation of the line is y=−0.7x+1.6.

Answer 2

Answer:
`\text{y}= -(5)/(7)\text{x}+(11)/(7)`

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Step-by-step explanation:

m = -5/7 = slope

(x1,y1) = (-2,-3) = the point the line goes through

Apply the point-slope formula and solve for y

`\text{y} - \text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y} - 3 = -(5)/(7)(\text{x}-(-2))\\\\\text{y} - 3 = -(5)/(7)(\text{x}+2)\\\\\text{y} - 3 = -(5)/(7)\text{x}-(5)/(7)*(2)\\\\`

`\text{y} - 3 = -(5)/(7)\text{x}-(10)/(7)\\\\\text{y}= -(5)/(7)\text{x}-(10)/(7) + 3 \\\\\text{y}= -(5)/(7)\text{x}-(10)/(7) + (21)/(7) \\\\\text{y}= -(5)/(7)\text{x}+(-10+21)/(7) \\\\\text{y}= -(5)/(7)\text{x}+(11)/(7) \\\\`

This equation is in slope-intercept form y = mx+b

m = -5/7 = slope

b = 11/7 = y intercept

An alternative way to write
`\text{y}= -(5)/(7)\text{x}+(11)/(7)` is to write y = (-5/7)x+11/7