![]() To find the equation of a line passing through the point \((3, 2)\) with a slope of \(-2\): Given that a line passes through the point \((3, 2)\) and has a slope of \(-2\), find its equation in both slope-intercept and point-slope forms. Writing Slope-intercept Form and Point-slope Form – Examples 2 Therefore, the equation of the line passing through the point \((-2, 7)\) with a slope of \(4\) is \(y = 4x + 15\) in slope-intercept form and \(y – 7 = 4(x + 2)\) in point-slope form. The point-slope form of a linear equation is \(y – y_1 = m(x – x_1)\), where \((x_1, y_1)\) is a point on the line and m is the slope. So, we can use the point-slope form to find the equation of the line. We have the slope \((m)\) as \(4\) and the point \((-2, 7)\) lies on the line. The slope-intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. To find the equation of a line passing through the point \((-2, 7)\) with a slope of \(4\): Writing Slope-intercept Form and Point-slope Form – Examples 1įind the equation of a line passing through the point \((-2, 7)\) with a slope of \(4\), and write it in both slope-intercept and point-slope forms. Overall, both slope-intercept form and point-slope form provide different ways of representing linear equations in two variables and can be useful in different contexts. This is the graph of the line represented by the equation in point-slope form. Plot the additional points on the line and draw a straight line through all the points. Step 6: Plot the additional points on the line For example, if the slope is positive, move up and to the right if the slope is negative, move down and to the right. To do this, you can start from the known point and move in the direction of the slope. Step 5: Use the slope to determine additional points on the line This is a point that you know is on the line represented by the equation in point-slope form. You can determine the coordinates of the point by looking at the values given in the equation. The point on the line, represented by \((x_1, y_1)\), is a known point on the line. Step 3: Determine the coordinates of the point on the line You can determine the slope by looking at the coefficient of \(x\) in the equation. The slope, represented by \(m\), is the rate at which the \(y\)-coordinate changes for every unit change in the \(x\)-coordinate. ![]() ![]() Write the equation in the form \(y – y_1 = m(x – x_1)\), where \(m\) is the slope of the line and \((x_1, y_1)\) is a point on the line. Point-Slope Form: Step 1: Write the equation This is the graph of the line represented by the equation in slope-intercept form. To do this, you can start from the \(y\)-intercept and move in the direction of the slope. This is the point where the line intersects the \(y\)-axis. Step 4: Plot the y-intercept on the y-axis You can determine the \(y\)-intercept by looking at the constant term in the equation. The \(y\)-intercept, represented by \(b\), is the point where the line crosses the \(y\)-axis. Step 3: Determine the \(y\)-intercept of the line Write the equation in the form \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\)-intercept. Here are the steps to write slope-intercept form and point-slope form Slope-Intercept Form: Step 1: Write the equation ![]() + Ratio, Proportion & Percentages PuzzlesĪ Step-by-step Guide to Write Slope-intercept Form and Point-slope Form.
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