Did you know?
Did you know that linear equations can be written in slope-intercept form? In this form, the equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept.
For example, let's consider three scenarios.
a. To find the equation of a line parallel to a line with slope 2 and passing through the point (-1,4), we can use the slope-intercept formula. Since the lines are parallel, the new line will also have a slope of 2. Plugging in the coordinates (-1,4) into the formula, we can solve for the y-intercept (b). The resulting equation will provide the desired linear equation.
b. If a line cuts the x-axis at 5 and the y-axis at -2, it means that its y-intercept is -2 (when x = 0) and its x-intercept is 5 (when y = 0). By substituting these values into the slope-intercept formula, we can determine the equation of this line.
c. To find the equation of a line perpendicular to a line with a gradient of -2 and passing through the point (-2,3), we can use a mathematical relationship between perpendicular lines. The slope of the new line will be the negative reciprocal of the gradient of the given line. By plugging in the coordinates (-2,3) into the formula and solving for the y-intercept (b), we can obtain the equation of the desired line.
Understanding slope-intercept form and utilizing it in various scenarios helps us describe and analyze linear equations more effectively.