Write the slope intercept for of the equation:
1 - slope = -5/4 , y intercept = -4
Ans: y = -5/4x - 4
2- Through (-1,4), slope = -2
Ans: y = -2x +2
3- Through (4,2) and (0,4)
Ans y= 1/2x -4
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To find the slope-intercept form of the equation, you need to know the slope (m) and the y-intercept (b).
1. For the equation with a slope of -5/4 and a y-intercept of -4, the slope-intercept form is y = -5/4x - 4.
2. For the equation passing through the point (-1,4) with a slope of -2, you can substitute the values into the point-slope form (y - y1 = m(x - x1)). Therefore, y - 4 = -2(x - (-1)). Simplifying this equation gives you y - 4 = -2x + 2. Next, rewrite the equation in slope-intercept form by isolating y, so it becomes y = -2x + 6.
3. For the equation passing through the points (4,2) and (0,4), you can find the slope (m) using the formula (m = (y2 - y1) / (x2 - x1)). Substituting the values, you get m = (2 - 4) / (4 - 0), which simplifies to m = -2 / 4 = -1/2. Using the slope-intercept form, substitute the slope (-1/2) and either point's coordinates into the equation y - y1 = m(x - x1). Let's use the point (0,4): y - 4 = -1/2(x - 0). Simplifying this equation gives y - 4 = -1/2x. Move the -4 to the other side of the equation, and the equation becomes y = -1/2x + 4. Hence, the slope-intercept form of the equation is y = 1/2x - 4.
To find the slope-intercept form of an equation, we need two pieces of information: the slope (m) and the y-intercept (b).
1 - In this case, the given slope is -5/4 and the y-intercept is -4. The slope is the coefficient of x, and the y-intercept is the constant term. So, the slope-intercept form of the equation becomes y = -5/4x - 4.
2 - Given the point (-1,4) and the slope -2, we can use the point-slope form of the equation, which is y - y1 = m(x - x1). Substituting the values, we have y - 4 = -2(x - (-1)). Simplifying this equation gives y - 4 = -2(x + 1). Now, we can convert this into slope-intercept form. Expanding the equation gives y - 4 = -2x - 2. Rearranging and combining like terms, we get y = -2x + 2.
3 - With two given points (4,2) and (0,4), we can find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the values gives m = (2 - 4) / (4 - 0) = -2 / 4 = -1/2. Now, we have the slope and one point (4,2). By using the point-slope form, we get y - 2 = -1/2(x - 4). Expanding this equation gives y - 2 = -1/2x + 2. Rearranging the equation and combining like terms, we get y = 1/2x - 4.