Question
Line g has an equation of y=2x+1 Line h includes the point (-5,2) and is perpendicular to line g. What is the equation of line h? Write the equation in slope-intercept form . Write the numbers in the equation as simplified proper fractions , improper fractions , or integers. square
Solution
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(203 Votos)
Paulinho
Mestre · Tutor por 5 anos
Resposta
To find the equation of line h, we need to determine its slope and use the point-slope form of a linear equation.Step 1: Find the slope of line g.The slope of line g is given by the coefficient of x in the equation y = 2x + 1. Therefore, the slope of line g is 2.Step 2: Find the slope of line h.Since line h is perpendicular to line g, its slope is the negative reciprocal of the slope of line g. Therefore, the slope of line h is -1/2.Step 3: Use the point-slope form to write the equation of line h.The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.Using the point (-5, 2) and the slope -1/2, we can substitute these values into the point-slope form:y - 2 = -1/2(x - (-5))Simplifying this equation, we get:y - 2 = -1/2(x + 5)Step 4: Convert the equation to slope-intercept form.To convert the equation to slope-intercept form, we need to solve for y:y = -1/2(x + 5) + 2Expanding and simplifying, we get:y = -1/2x - 5/2 + 2Combining like terms, we get:y = -1/2x - 1/2Therefore, the equation of line h in slope-intercept form is:y = -1/2x - 1/2