For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. x - intercept (-3, 0), y-intercept (0, 5)

Verified step by step guidance

1. Identify the two points given: the x-intercept (-3, 0) and the y-intercept (0, 5). These points lie on the line.
2. Calculate the slope \( m \) of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substitute the points \((-3, 0)\) and \((0, 5)\) into the formula.
3. Use the slope-intercept form equation \( y = mx + b \). Since the y-intercept is given as \( (0, 5) \), the value of \( b \) is 5. Substitute \( m \) and \( b \) into the equation.
4. Write the slope-intercept form equation explicitly with the values of \( m \) and \( b \) found in the previous steps.
5. To write the equation in standard form \( Ax + By = C \), rearrange the slope-intercept form by moving all terms to one side and clearing any fractions if necessary.

Key Concepts

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It expresses the equation of a line by showing how y changes with x, making it easy to graph and understand the line's behavior.

Finding the Slope from Intercepts

The slope of a line can be found using two points, such as the x-intercept and y-intercept, with the formula m = (y2 - y1) / (x2 - x1). This slope represents the rate of change between the two intercepts.

Standard Form of a Line

The standard form of a line is Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for solving systems of equations and provides a clear, general representation of a line.