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)

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Identify the two points given: the x-intercept (-3, 0) and the y-intercept (0, 5). These points lie on the line.

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.

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.

Write the slope-intercept form equation explicitly with the values of $ m $ and $ b $ found in the previous steps.

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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