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sattari [20]
2 years ago
11

Write the slope-intercept form of the equation of the line described. Through (-1,-1) parallel to y=6x-2

Mathematics
1 answer:
Alex17521 [72]2 years ago
7 0

Answer:

\boxed {\boxed {\sf y= 6x+5}}

Step-by-step explanation:

We are asked to find the slope-intercept equation of a line. Slope-intercept form is one way to write the equation of a line. It is:

y=mx+b

Where m is the slope and b is the y-intercept.

We are given a point (-1, -1) and the line is parallel to the line y= 6x-2. Since the line is parallel to the other line, they have the same slope, which is 6. We have a point and a slope, so we should use the point-slope formula to find the equation of the line.

y-y_1= m (x-x_1)

Here, m is the slope and (x₁, y₁) is the point. We know the slope is 6 and the point is (-1, -1). Therefore:

  • m= 6
  • x₁= -1
  • y₁= -1

Substitute the values into the formula.

y- -1 = 6(x- -1) \\y+1= 6(x+1)

Distribute the 6. Multiply each value inside the parentheses by 6.

y+1 = (6*x)+ (6*1) \\y+1= 6x+6

Slope-intercept form requires y to be isolated. 1 is being added to y. The inverse of addition is subtraction. Subtract 1 from both sides.

y+1-1=6x+6-1 \\y= 6x+5

The equation of the line in slope-intercept form is <u>y=6x+5</u>

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45

Step-by-step explanation:

Triangles equal up to 180 degrees therefore you do the following to solve this equation. So you have 80 and 55. So you add 80 to 55 and you get 135. Now you subtract 180 by 135 and that equals 45. So x=45. I will write it out as well.

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Which equations represents the line that pases through points (1,-5) and (3, -17)?
Pachacha [2.7K]

Answer:

y= -6x +1

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx +c, where m is the gradient (or slope) and c is the y-intercept.

In order to find the equation of a line, you would need 2 things:

① Gradient (← can be found)

② Coordinate (✓ we have 2 coordinates here)

To find the gradient, use the gradient formula below:

gradient =  \frac{y1 - y2}{x1 - x2}

m =  \frac{ - 5 - ( - 17)}{1 - 3}  \\ m =  \frac{ - 5 + 17}{ - 2}  \\ m =  \frac{12}{ - 2}  \\ m =  - 6

Substitute the value of m into the equation:

y= -6x +c

To find the value of c, substitute a pair of coordinates.

When x=1, y= -5,

-5= -6(1) +c

c -6= -5

c= 6 -5

c= 1

Thus, the equation of the line is y= -6x +1.

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2 years ago
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