Slope and y-intercept

The equation of the line is y = -12x + 18. The number multiplying x is -12, so the coefficient of x is -12. In the form y = mx + c, m is also the slope; hence the slope here is -12. The number 18 is the constant term (y-intercept), not the coefficient of x. Exam tip: Always include the sign with the coefficient of x.

In the form \(y=mx+c\), \(c\) is the \(y\)-intercept because substituting \(x=0\) gives \(y=c\). In \(y=3x-4\), the constant term is \(-4\), so its \(y\)-intercept is \(-4\). In \(y=-4x+3\), \(-4\) is the slope, not the \(y\)-intercept. Exam tip: To find the \(y\)-intercept, put \(x=0\) in the equation.

In the equation \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope. In \(y=7x-6\), the coefficient of \(x\) is 7, so its slope is 7. In \(y=x+7\), the slope is 1; 7 is only the y-intercept. Exam tip: identify the coefficient of \(x\), not the constant term, to find the slope.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. The given line can be written as \(y=-9x+22\). Hence, \(m=-9\) and \(c=22\). Option B incorrectly ignores the negative sign of the coefficient of \(x\). Exam tip: Always retain the sign of the coefficient of \(x\) while identifying the slope.

Compare the line with slope-intercept form \(y=mx+c\). Since \(y=7-10x=-10x+7\), the coefficient of \(x\) is \(-10\), so the slope is \(-10\); the constant term is \(7\), so the y-intercept is \(7\). Option C has the correct y-intercept but misses the negative sign of the slope. Exam tip: in \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept.

In the form y = mx + c, m represents the slope, that is, the change in y for a one-unit change in x. Therefore, in (y=mx-8), m is the slope. Here, -8 is the y-intercept; it shows where the line meets the y-axis. Exam tip: In y = mx + c, identify m as the slope and c as the y-intercept.

To find the \(y\)-intercept, put \(x=0\). Then \(y=-0-12=-12\), so the line crosses the \(y\)-axis at \(-12\). Here, \(-1\) is the slope, not the \(y\)-intercept. Exam tip: in \(y=mx+c\), \(c\) is the \(y\)-intercept.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope. In \(y=16x+5\), the coefficient of \(x\) is 16, so the slope is 16. The number 5 is the y-intercept, not the slope. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is always the slope.

In the line \(y=-15\), the value of \(y\) remains constant for every value of \(x\), so it is a horizontal line parallel to the x-axis. For a horizontal line, the change in \(y\) is \(0\), hence its slope is \(0\). The value \(-15\) is the y-intercept, not the slope. Exam tip: Every line of the form \(y=c\) has slope \(0\).

In the form \(y=mx+c\), \(c\) is the \(y\)-intercept. At the point where the line meets the \(y\)-axis, \(x=0\). Substituting the given point \((0,6)\) gives \(6=m(0)+c\), so \(c=6\). It would be \(-6\) only if the line met the \(y\)-axis at \((0,-6)\). Exam tip: in \(y=mx+c\), the constant term \(c\) directly gives the \(y\)-intercept.

In the form \(y=mx+c\), \(c\) is the y-intercept, that is, the y-coordinate where the line meets the y-axis. The given point is \((0,-9)\), so \(c=-9\). Choosing \(9\) would ignore the negative sign. Exam tip: every point on the y-axis has x-coordinate 0.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=9\) and \(c=-2\) gives \(y=9x-2\). Option C has slope 9, but its \(y\)-intercept is \(+2\), so it is not correct. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=-6\) and \(c=-8\) gives \(y=-6x-8\). In option C, the slope and intercept values are interchanged, while option D has a \(y\)-intercept of \(+8\). Exam tip: In \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is the \(y\)-intercept.

A line in the form \(y=mx+c\) has \(c\) as its \(y\)-intercept. Here, \(c=2\), so the \(y\)-intercept is \(2\); the line meets the \(y\)-axis at \((0,2)\). \(\frac{9}{4}\) is the slope, not the intercept. Exam tip: put \(x=0\) to find the \(y\)-intercept.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the y-intercept. Here, the coefficient of \(x\) is \(-\frac{5}{9}\), so the slope is \(-\frac{5}{9}\). The number \(8\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), identify the number multiplying \(x\) as the slope.

At every point on the y-axis, \(x=0\). Substituting \(x=0\) in \(y=7x+20\) gives \(y=7(0)+20=20\). Therefore, the line cuts the y-axis at \(y=20\). Here, \(7\) is the slope, not the y-intercept. Exam tip: in \(y=mx+c\), the y-intercept is \(c\).

A line in the form \(y=mx+c\) has slope \(m\). Here, the coefficient of \(x\) is \(-10\), so the slope is \(-10\) and its sign is negative. A zero slope occurs only when \(m=0\). Exam tip: In \(y=mx+c\), check the coefficient of \(x\) to identify the sign of the slope quickly.

A line in the form y = mx + c has slope m. Here, the coefficient of x is 14, so the slope is 14 and its sign is positive. A negative slope would require the coefficient of x to be less than 0. Exam tip: In y = mx + c, look at the coefficient of x to identify the sign of the slope quickly.

Using y = mx + b, identify the coefficient of x as the slope and the constant as the y-intercept. Here y = 0x - 7, so m = 0 and b = -7. The line therefore has no upward or downward tilt and crosses the y-axis at (0, -7). Option A is correct. Option B reverses the roles of the terms, whereas C and D incorrectly make the negative constant positive.

The equation is y = 21 − 8x, which can also be written as y = −8x + 21. The number multiplying x is −8, so the coefficient of x is −8. The term without x is 21, so it is the constant term. Option B misses the negative sign. Exam tip: a negative sign before a term is part of its coefficient.

At every point on the \(y\)-axis, \(x=0\). Substituting \(x=0\) in \(y=10-2x\) gives \(y=10\). Hence, the line cuts the \(y\)-axis at \((0,10)\). The point \((10,0)\) may relate to the \(x\)-intercept, but it is not on the \(y\)-axis. Exam tip: to find a \(y\)-intercept, always put \(x=0\).

A line parallel to the x-axis has slope 0, so its equation is \(y=c\). With y-intercept \(-4\), \(c=-4\), giving \(y=-4\). In contrast, \(x=-4\) is a vertical line. Exam tip: every equation of the form \(y=c\) is horizontal.

A line in the form y=mx+c has slope m, which gives the rate of change. Here, m=11, so an increase of 1 in x increases y by 11. The number 13 is the y-intercept, not the amount of increase. Exam tip: In y=mx+c, the coefficient of x is the slope.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope. In \(y=\frac{4}{3}x-6\), the coefficient of \(x\) is \(\frac{4}{3}\), so the slope is \(\frac{4}{3}\). The value \(-6\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), the coefficient of \(x\) is always the slope.

In the form \(y=mx+c\), \(c\) is the y-intercept. Here, \(c=5\), so the line crosses the y-axis at \((0,5)\), and its y-intercept is \(5\). \(-\frac{3}{8}\) is the slope, not the y-intercept. Exam tip: put \(x=0\) to find the y-intercept.