Slope and y-intercept

In the form \(y=mx+c\), \(c\) is the y-intercept, meaning the value of \(y\) when \(x=0\). At the given point \((0,-2)\), \(y=-2\); therefore, \(c=-2\). Option \(2\) results from a sign error. Exam tip: in \(y=mx+c\), the y-intercept is directly \(c\).

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 \(c=-2\) gives \(y=6x-2\). Option C has slope 6, but its \(y\)-intercept is \(+2\), so it is not correct. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is 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. Substituting \(m=-1\) and \(c=-5\) gives \(y=-x-5\). Option D has slope \(-1\), but its \(y\)-intercept is \(+5\). 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 y-intercept \(c\). Here, \(c=-4\), so the y-intercept is \(-4\). The value \(\frac{5}{3}\) is the slope, not the y-intercept. Exam tip: put \(x=0\) to find the y-intercept.

A line in slope-intercept form is \(y=mx+c\), where \(m\) is the slope. In \(y=-\frac{2}{5}x+9\), the coefficient of \(x\) is \(-\frac{2}{5}\), so the slope is \(-\frac{2}{5}\). The number \(9\) is the y-intercept, not the slope, and \(\frac{2}{5}\) incorrectly omits the negative sign. Exam tip: in \(y=mx+c\), identify the coefficient of \(x\) as the slope.

At every point on the (y)-axis, (x=0). Substituting (x=0) in (y=3x+12) gives (y=3(0)+12=12). Hence, the line cuts the (y)-axis at (y=12). Here, (3) is the slope, not the (y)-intercept. Exam tip: in the form (y=mx+c), (c) is always the (y)-intercept.

A line in the form y = mx + c has slope m, the coefficient of x. Here, m = -6, which is less than 0; therefore, the slope is negative. A zero slope would require the coefficient of x to be 0, as in y = 18. Exam tip: In y = mx + c, identify the slope by looking at the coefficient of x.

The slope-intercept form of a line is y=mx+c, where the coefficient of x, m, is the slope. Here m=11, and 11 is greater than zero, so the slope is positive. A negative slope would require the coefficient of x to be less than zero. Exam tip: In y=mx+c, identify the slope by looking at the coefficient of x.

A line written as y = mx + b has slope m and y-intercept b. Comparing y = 0x - 10 with this form gives m = 0 and b = -10. Thus the graph is a horizontal line crossing the y-axis at (0, -10). Option A states both values correctly. Option B interchanges the coefficient and constant, while options C and D incorrectly change the signs. The zero coefficient means there is no rise as x changes.

The given expression is (y=14-2x), which can be written in standard order as (y=-2x+14). The number multiplying (x) is -2, so the coefficient of (x) is -2. The term without (x) is 14; hence, the constant term is 14. In option B, the sign of the coefficient is incorrect. Exam tip: Always include the positive or negative sign with a coefficient.

In the form \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope. Here, in \(y=4x+3\), \(m=4\), so the slope is 4. The number 3 is the \(y\)-intercept, not the slope. Exam tip: identify the coefficient of \(x\) to find the slope.

In the standard form \(y=mx+c\), \(c\) is the \(y\)-intercept because putting \(x=0\) gives \(y=c\). Here, in \(y=5x-6\), \(c=-6\); therefore, the \(y\)-intercept is \(-6\). The value \(5\) is the slope, not the intercept. Exam tip: To find the \(y\)-intercept, set \(x=0\).

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope. In \(y=-3x+8\), the coefficient of \(x\) is \(-3\), so the slope is \(-3\). The number \(8\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), the coefficient of \(x\) gives the slope directly.

Write the line in slope-intercept form: \(y=-4x+11\). In \(y=mx+c\), the coefficient of \(x\), namely \(m\), is the slope. Therefore, the slope is \(-4\). Here, 11 is the y-intercept, not the slope. Exam tip: In \(y=a+bx\), the coefficient \(b\) of \(x\) is the slope.

The y-intercept is the y-value where the line meets the y-axis, so x=0. Substituting x=0 in y=2x+9 gives y=2(0)+9=9. Therefore, 9 is correct. The number 2 is the coefficient of x, or the slope, not the y-intercept. Exam tip: In the form y=mx+c, the constant term c is the y-intercept.

The slope-intercept form of a line is y=mx+c, where the coefficient of x, m, is the slope. In y=-7x+1, m=-7, so the slope is -7. The number 1 is the y-intercept, not the slope. Exam tip: In y=mx+c, identify the number multiplying x to find the slope.

A line in the form \(y=mx+c\) has slope \(m\), the coefficient of \(x\). In \(y=0x+14\), the coefficient of \(x\) is \(0\), so the slope is \(0\). The number \(14\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), identify the coefficient of \(x\) to find the slope.

In the linear equation y=mx+c, m is the coefficient of x and represents the slope of the line. The constant c does not give the slope; it represents the y-intercept. Exam tip: identify the coefficient multiplying x to find m.

In the linear form \(y=mx+c\), \(c\) is the constant term and represents the y-intercept. On putting \(x=0\), we get \(y=c\), so the graph meets the y-axis at \(c\). In contrast, \(m\) represents the slope, not the y-intercept. Exam tip: set \(x=0\) 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. Substituting \(m=5\) and \(c=2\) gives \(y=5x+2\). Therefore, option C is correct. Option B has slope 5, but its \(y\)-intercept is \(-2\). Exam tip: in \(y=mx+c\), the coefficient of \(x\) is the slope and the constant term is the \(y\)-intercept.