Question

Graph the line passing through the point (−1,−3) that has a slope of m=4

Answer 1

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Answer:
`\textsf{y = 4x + 1, look at attached file for graph}`

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Given:
`\textsf{Slope = 4, Passes through (-1, -3)}`

Find:
`\textsf{The line that captures this information. Graph the equation}`

Solution: The first thing that we need to do is plug in the information into the point-slope formula which we would then distribute, simplify, and solve for y to convert he formula into slope-intercept form.

Plug in the values

• 
  `y - y_1 = m(x - x_1)`

• 
  `y - (-3) = 4(x - (-1))`

Simplify the expression

• 
  `y + 3 = 4(x + 1)`

Distribute

• 
  `y + 3 = (4 * x) + (4 * 1)`

• 
  `y + 3 = 4x + 4`

Subtract 3 from both sides

• 
  `y + 3 - 3 = 4x + 4 - 3`

• 
  `y = 4x + 4 - 3`

• 
  `y = 4x + 1`

Now that we have the equation fully created and simplified we can begin to plot the equation. So we know that the y-intercept would be (0, 1) since the equation states that and we also know that we would have another point at (-1, -3) which we can also draw and then we can just draw a line in-between them.

Answer 2

Equation: y = 4x + 1

See the attached for the graph.

Explanation:

Given:

• a slope of 4
• the point (-1, -3)

Point-Slope Form: y - y₁ = m(x - x₁)

where:

• m is the slope
• (x₁, y₁) is a given point

1. Substitute the given values into the formula:

⇒ y - y₁ = m(x - x₁)

⇒ y - (-3) = 4(x - (-1) [simplify]

⇒ y + 3 = 4(x + 1) [distribute 4 through the parentheses]

⇒ y + 3 = 4x + 4 [subtract 3 from both sides]

⇒ y + 3 - 3 = 4x + 4 - 3

⇒ y = 4x + 1

2. Check your work:

⇒ y = 4x + 1

⇒ -3 = 4(-1) + 1

⇒ -3 = -4 + 1

⇒ -3 = -3 ✔

The equation of the line is: y = 4x + 1