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 x-intercept and y-intercept: The x-intercept is (-3, 0) and the y-intercept is (0, 5).
2. Use the intercepts to find the slope (m) of the line: The formula for slope is m = (y_2 - y_1) / (x_2 - x_1).
3. Substitute the intercepts into the slope formula: m = (5 - 0) / (0 - (-3)).
4. Write the equation in slope-intercept form (y = mx + b) using the slope and y-intercept: y = mx + 5.
5. Convert the slope-intercept form to standard form (Ax + By = C) by rearranging the terms.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is useful for quickly identifying the slope and y-intercept, making it easier to graph the line. To convert from standard form to slope-intercept form, one typically solves for y.

Standard Form

The standard form of a linear equation is given as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is beneficial for analyzing the relationship between x and y and is often used in systems of equations. To convert from slope-intercept form to standard form, one rearranges the equation to fit this format.

Intercepts

Intercepts are points where a line crosses the axes of a graph. The x-intercept is the point where the line intersects the x-axis (y=0), while the y-intercept is where it intersects the y-axis (x=0). Knowing the intercepts allows for the easy construction of the line's equation and helps in graphing the line accurately.