What is the equation of the line in slope-intercept form?

Question

Enter your answer in the boxes.

y =
x +

$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Line on a coordinate plane. Line runs through points begin ordered pair negative 3 comma 0 end ordered pair and begin ordered pair 0 comma 4.

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points provided: \((-3, 0)\) and \((0, 4)\).

Step 1: Calculate the Slope (m)

The formula for the slope (m) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((x_1, y_1) = (-3, 0)\) and \((x_2, y_2) = (0, 4)\):

\[ m = \frac{4 - 0}{0 - (-3)} = \frac{4}{3} \]

Step 2: Use the Point-Slope Form to Find the y-intercept (b)

Now that we have the slope \(m = \frac{4}{3}\), we can use one of the points to determine the y-intercept (b). We will use the point \((0, 4)\) because it is directly the y-intercept.

Since the point \((0, 4)\) represents the y-intercept:

\[ b = 4 \]

Step 3: Write the Equation in Slope-Intercept Form

Now we can write the equation of the line using the slope \(m\) and the y-intercept \(b\):

\[ y = \frac{4}{3}x + 4 \]

Step 4: Fill in the Boxes

Thus, the final answer in slope-intercept form is:

y = \( \frac{4}{3} \) x + 4

So, we can fill in the boxes as follows:

y = \(\frac{4}{3}\)
x + \(4 \)

Make sure to enter the fraction and constant correctly in the available input fields.