Respuesta :

Esther

Answer:

Equation: y = 4x + 1

See the attached for the graph.

Step-by-step 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

Ver imagen Esther
igoroleshko156

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Answer:  [tex]\textsf{y = 4x + 1, look at attached file for graph}[/tex]

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Given:  [tex]\textsf{Slope = 4, Passes through (-1, -3)}[/tex]

Find: [tex]\textsf{The line that captures this information. Graph the equation}[/tex]

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

  • [tex]y - y_1 = m(x - x_1)[/tex]
  • [tex]y - (-3) = 4(x - (-1))[/tex]

Simplify the expression

  • [tex]y + 3 = 4(x + 1)[/tex]

Distribute

  • [tex]y + 3 = (4 * x) + (4 * 1)[/tex]
  • [tex]y + 3 = 4x + 4[/tex]

Subtract 3 from both sides

  • [tex]y + 3 - 3 = 4x + 4 - 3[/tex]
  • [tex]y = 4x + 4 - 3[/tex]
  • [tex]y = 4x + 1[/tex]

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.

Ver imagen igoroleshko156