(-2, 5) and (4, -7). Write an equation for the line that passes through (1, 3) and is parallel to line ℓ. Leave in slope-intercept form.

Answer 1

To find the equation of a line that passes through the point (1,3)(1, 3) and is parallel to the line ℓ\ell passing through (−2,5)(-2, 5) and (4,−7)(4, -7), follow these steps:

Step 1: Find the slope of line ℓ\ell

The slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the formula:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}Substitute the points (−2,5)(-2, 5) and (4,−7)(4, -7) into the formula:

m=−7−54−(−2)=−126=−2m = \frac{-7 - 5}{4 - (-2)} = \frac{-12}{6} = -2Thus, the slope of line ℓ\ell is m=−2m = -2.

Step 2: Use the same slope for the parallel line

Since parallel lines have the same slope, the slope of the line passing through (1,3)(1, 3) is also m=−2m = -2.

Step 3: Use point-slope form to write the equation

We can use the point-slope form of the equation of a line, which is:

y−y1=m(x−x1)y - y_1 = m(x - x_1)where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. Here, m=−2m = -2 and (x1,y1)=(1,3)(x_1, y_1) = (1, 3).

Substitute these values into the point-slope formula:

y−3=−2(x−1)y - 3 = -2(x - 1)Step 4: Simplify to slope-intercept form

Distribute −2-2 on the right-hand side:

y−3=−2x+2y - 3 = -2x + 2Now, add 3 to both sides to solve for yy:

y=−2x+5y = -2x + 5Final Answer:

The equation of the line passing through (1,3)(1, 3) and parallel to line ℓ\ell is:

y=−2x+5y = -2x + 5

Answer 2

To solve this, we'll first determine the slope of line l, which passes through (-2, 5) and (4, -7). Then, we'll write the equation of a line that is parallel to l and passes through (1,3).

1) Find the slope of line l

The formula for the slope (m) is:

m = (y2 - y1) / (x2 - x1)​​

Substituting the points (-2, 5) and (4, -7):

m = (-7 - 5) / (4- -2) = -12/6 = -2

The slope of l is m= -2

2) Write the equation of the new line

Since the new line is parallel to l, it has the same slope: m= -2. Using the point-slope form of a line equation:

y-y1=m(x-x1)

Substitute x1 = 1, y1 = 3, m = -2:

y-3= -2(x-1)

Simplify to slope-intercept form (y=mx+b):

y-3=-2x+2

y=-2x+5

Final Answer:

The equation of the line is: y= -2x + 5

Answer 3

Hi Jessenia,

First of all, remember that parallel lines have the same slope, so if you get the slope of the first, you will have the slope of the second. Formula for slope m with two points:

m = (y2 - y1) / (x2 - x1)

m = (-7 - 5) / (4- -2) = -12/6 = -2

Now, slope-intercept form is y = mx + b, where m is slope, x and y are given ordered pair, and b is y-intercept. Here:

x = 1

y = 3

m = -2

Thus:

3 = -2(1) + b

3 = -2 + b

b = 5

Final equation:

y = -2x + 5

I hope this helps.