Final answer:
The equation of the line with an x-intercept of -4 and a y-intercept of 3 is y = -3/4x + 3 in slope-intercept form, y - 3 = -3/4x in point-slope form, and 3x + 4y = 12 in standard form.
Step-by-step explanation:
To find the equation of a line with an x-intercept of -4 and a y-intercept of 3, we first determine the slope of the line. The slope (m) can be calculated using the rise over run formula between the two intercepts. In this case, moving from the x-intercept at (-4, 0) to the y-intercept at (0, 3), we get a rise of 3 and a run of 4.
Therefore, the slope is -3/4 (since we moved to the right and up, the x-value increased and the y-value decreased, which means the slope is negative).
The slope-intercept form of the equation is y = mx + b, where m is the slope and b is the y-intercept. For this line, the equation is y = -3/4x + 3.
To write the equation in point-slope form, we can use the formula y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope. Using the y-intercept point (0, 3), the equation would be y - 3 = -3/4(x - 0), which simplifies to y - 3 = -3/4x.
The standard form of a line's equation is Ax + By = C, where A, B, and C are integers. Multiplying both sides of the slope-intercept form by 4 to eliminate the fraction and then moving the terms around gives us 3x + 4y = 12.