a) 𝑦 = 5/2𝑥 − 6; slope: 5/2; y-intercept: -6
b) 𝑦 = (5/2)𝑥 − 6; slope: 5/2; y-intercept: -6
c) 𝑦 = -5/2𝑥 + 6; slope: -5/2; y-intercept: 6
d) 𝑦 = -5/2𝑥 - 6; slope: -5/2; y-intercept: -6
The correct answer is d) 𝑦 = -5/2𝑥 - 6; slope: -5/2; y-intercept: -6.
a) The equation 𝑦 = 5/2𝑥 − 6 has a slope of 5/2 and a y-intercept of -6. The slope of 5/2 means that for every 2 units increase in the x-coordinate, the y-coordinate would increase by 5 units. The y-intercept of -6 represents the point where the graph intersects the y-axis, which is when x = 0, so y would equal -6.
b) The equation 𝑦 = (5/2)𝑥 − 6 is the same as equation (a). It has a slope of 5/2 and a y-intercept of -6.
c) The equation 𝑦 = -5/2𝑥 + 6 has a slope of -5/2 and a y-intercept of 6. The slope of -5/2 means that for every 2 units increase in the x-coordinate, the y-coordinate would decrease by 5 units. The y-intercept of 6 represents the point where the graph intersects the y-axis, which is when x = 0, so y would equal 6.
d) The equation 𝑦 = -5/2𝑥 - 6 has a slope of -5/2 and a y-intercept of -6. The slope of -5/2 means that for every 2 units increase in the x-coordinate, the y-coordinate would decrease by 5 units. The y-intercept of -6 represents the point where the graph intersects the y-axis, which is when x = 0, so y would equal -6.
To find the slope and y-intercept of each equation, we can use the slope-intercept form, which is in the form 𝑦 = 𝑚𝑥 + 𝑏. In this form, 𝑚 represents the slope and 𝑏 represents the y-intercept.
a) 𝑦 = 5/2𝑥 − 6
In this equation, the slope is 5/2 and the y-intercept is -6.
b) 𝑦 = (5/2)𝑥 − 6
This equation is the same as the equation in part a) since multiplying a number by 1 does not change its value. So, the slope is still 5/2 and the y-intercept is still -6.
c) 𝑦 = -5/2𝑥 + 6
In this equation, the slope is -5/2 and the y-intercept is 6.
d) 𝑦 = -5/2𝑥 - 6
This equation is similar to the equation in part c) except for the sign of the y-intercept. So, the slope is still -5/2 and the y-intercept is still -6.